Range Frequency Theory

To understand the pattern of results concerning schifts in the temporal bisection point, We have to check the distribution of stimuli within the sets firstly.

sumfreq_exp1_sub1 <-  dat_exp1 %>% filter(NSub == 1) %>% group_by(cond, curDur) %>% summarise(count = n())
count_exp1 <- sum(sumfreq_exp1_sub1$count)/2
sumfreq_exp1_sub1$exp <- 'Exp1'
sumfreq_exp1_sub1$freq <- sumfreq_exp1_sub1$count/count_exp1*100

# rename columns
fig_exp1_sub1_dist <- ggplot(data=sumfreq_exp1_sub1, aes(x=curDur, y=count, fill=cond)) +
  geom_bar(stat="identity", position=position_dodge()) +
   #geom_smooth(method="loess",se = FALSE)+
  xlab('Durations (ms)') + ylab('Counts of trials for each participant') +
   scale_x_continuous(breaks=seq(0, 1600, 200)) +
    scale_color_manual(values = c('gray','black')) +
    scale_fill_manual(values = c('gray','black')) +mytheme+ facet_wrap(~cond)

fig_exp1_sub1_dist

if (saveFigure == TRUE){
  ggsave("figures/fig_exp1_sub1_dist.svg", fig_exp1_sub1_dist)
}

plot the distribution of stimulus set

mDist_exp1 <-  dat_exp1 %>% filter(NSub == 1) %>% dplyr::group_by(cond) %>%
summarise(m_cDur = mean(curDur), n = dplyr::n(),
cDur_se = sd(curDur)/sqrt(n-1))
mDist_exp1

plot_mDist_exp1 <- ggplot(mDist_exp1,aes(cond, m_cDur, color = cond, fill = cond))+
geom_bar(stat='identity') +
geom_errorbar(aes(ymin = m_cDur - cDur_se, ymax = m_cDur + cDur_se), width =0.5) +
labs(x = " ", y = "Mean of Durations (ms)") +
scale_color_manual(values = c('gray','black')) +
scale_fill_manual(values = c('gray','black')) +
theme(legend.position = "none", legend.title = element_blank())+
theme(panel.grid.major=element_line(colour=NA))+
theme(axis.text.y = element_text(size=26,colour = "black"),
axis.text.x   = element_text(size=26, colour = "black"),
axis.title.y  = element_text(size=26, colour = "black"),
axis.title.x  = element_text(size=26, colour = "black"),
panel.background = element_blank(),
panel.grid.major = element_blank(),
panel.grid.minor = element_blank(),
axis.line = element_line(colour = "black"))

if (saveFigure == TRUE){
ggsave("figures/plot_mDist_exp1.png", plot_mDist_exp1, 
       width = 4.5, height=5.5)
}
plot_mDist_exp1

fit psychometric functions

fits_exp1 = quickpsy(dat_exp1, x = curDur, k =RP, prob = .5,
                grouping = .(cond, NSub), thresholds = FALSE)

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head(fits_exp1$thresholds)

fits_exp1_all = quickpsy(dat_exp1, x = curDur, k =RP, prob = .5, grouping = .(cond))
fits_exp1_all

NULL

# plot fitted function
 plot_fit_exp1 <- plot(fits_exp1_all) +  
  labs(x = "Durations (ms)", y = "Proportion of 'Long' responses") +
    scale_color_manual(values = c('gray','black')) +
    scale_fill_manual(values = c('gray','black')) +
    theme(legend.position = c(0.7, 0.2), legend.title = element_blank())

Ignoring unknown aesthetics: x

  plot_fit_exp1

  #+theme_classic()
if (saveFigure == TRUE){
  ggsave("figures/pse_exp1.png", plot_fit_exp1)
}

aic(fits_exp1_all)

ypred(fits_exp1_all)

======= ##slope From the equation of psychometric fuction (PF), we can easily obtained the point of subjective equality (PSE, \(\alpha\)) and just noticeable difference (JND). Notice, the JND is defined by the difference between thresholds P=0.5 and P=0.75, so we have \[JND = log3/ \beta\] Therefore,

\[\beta = 3 / e^{JND} \]

exp1_all_thres<- fits_exp1_all$thresholds
exp1_all_thres$slope = 3/exp(exp1_all_thres$thre/1000) #slope
exp1_all_thres

exp1_thres<- fits_exp1$thresholds
exp1_thres$slope = 3/exp(exp1_thres$thre/1000) #slope
exp1_thres

list all of the parameter for each subjects

par_exp1 = fits_exp1$par %>% 
  dplyr::select(-parinf,-parsup) %>%
  spread(parn, par) %>%   
  rename(pse =p1, jnd = p2)  # rename columns
par_exp1$slope = 3/exp(par_exp1$jnd/1000) #slope

par_exp1

mpars_exp1 = par_exp1%>% 
  group_by(cond) %>%
  summarise(m_pse = mean(pse), m_jnd = mean(jnd),  m_slope = mean(slope), n = n(),
            pse_se = sd(pse)/sqrt(n-1), 
            jnd_se = sd(jnd)/sqrt(n-1),
            slope_se = sd(slope)/sqrt(n-1)) 

mpars_exp1

======= ##Export for JASP

List all of the parameters for exp1 and export data for JASP

exp1_jasp <- par_exp1%>% 
  unite(pse.jnd.slope, pse, jnd, slope)%>%
  spread(cond, pse.jnd.slope)%>%
  separate(`PS`, c("PSC_pse", "PSC_jnd","PSC_slope"), sep = "_")%>%
  separate(`NS`, c("NSC_pse", "NSC_jnd","NSC_slope"), sep = "_")

exp1_jasp

plot PSE

plot_pse_exp1 <- ggplot(mpars_exp1,aes(cond, m_pse, color = cond, fill = cond))+
  geom_bar(stat='identity') + 
  geom_errorbar(aes(ymin = m_pse - pse_se, ymax = m_pse + pse_se), width =0.5) +
    geom_signif(comparisons=list(c("PS", "NS")), annotations="*", y_position = 1150, tip_length = 0, vjust=0.4, color = 'black') +
   labs(x = " ", y = "Mean PSE (ms)") +
  coord_cartesian(ylim = c(0,1300)) +
    scale_color_manual(values = c('gray','black')) +
    scale_fill_manual(values = c('gray','black')) +
  theme(legend.position = "none")

plot_pse_exp1

plot JND

plot_jnd_exp1 <- ggplot(mpars_exp1,aes(cond, m_jnd, color = cond, fill = cond))+
  geom_bar(stat='identity') + 
  geom_errorbar(aes(ymin = m_jnd - jnd_se, ymax = m_jnd + jnd_se), width =0.5) +
  labs(x = " ", y = "Mean JND (ms)") +
  coord_cartesian(ylim = c(0,400))+
  scale_color_manual(values = c('gray','black')) +
  scale_fill_manual(values = c('gray','black')) + theme(legend.position = "none")

plot_jnd_exp1

ANOVA and T-test

Anova_exp1_pse<- ezANOVA(data = par_exp1, dv= pse, wid=NSub, within=.(cond))

Converting "NSub" to factor for ANOVA.

Anova_exp1_pse

$ANOVA

NA

Anova_exp1_jnd<- ezANOVA(data = par_exp1, dv= jnd, wid=NSub, within=.(cond))

Converting "NSub" to factor for ANOVA.

Anova_exp1_jnd

$ANOVA

NA

Anova_exp1_slope<- ezANOVA(data = par_exp1, dv= slope, wid=NSub, within=.(cond))

Converting "NSub" to factor for ANOVA.

Anova_exp1_slope

$ANOVA

NA

Range Frequency Theory

A particular focus is the distribution of stimuli within the sets to be judged. To understand the pattern of results concerning schifts in the temporal bisection point, We have to check the frequency of the sets firstly.

sumfreq_exp2_sub1 <-  dat_exp2 %>% filter(NSub == 1) %>% group_by(cond, curDur) %>% summarise(count = n()) 
count_exp2 <- sum(sumfreq_exp2_sub1$count)/2
sumfreq_exp2_sub1$exp <- 'Exp2'
sumfreq_exp2_sub1$freq <- sumfreq_exp2_sub1$count/count_exp2*100
fig_exp2_sub1_dist <- ggplot(data=sumfreq_exp2_sub1, aes(x=curDur, y=count, fill=cond)) +
  geom_bar(stat="identity", position=position_dodge()) + 
  xlab('Durations (ms)') + ylab('Counts of trials for each participant') +
  scale_x_continuous(breaks=seq(0, 1600, 200)) +
  scale_color_manual(values = c('gray','black')) +
  scale_fill_manual(values = c('gray','black')) +mytheme

fig_exp2_sub1_dist

mDist_exp2 <-  dat_exp2 %>% filter(NSub == 1) %>% dplyr::group_by(cond) %>%
  summarise(m_cDur = mean(curDur), n = dplyr::n(),
            cDur_se = sd(curDur)/sqrt(n-1))
mDist_exp2

plot_mDist_exp2 <- ggplot(mDist_exp2,aes(cond, m_cDur, color = cond, fill = cond))+
  geom_bar(stat='identity') +
  geom_errorbar(aes(ymin = m_cDur - cDur_se, ymax = m_cDur + cDur_se), width =0.5) +
  #geom_text(aes(label=paste("(",m_cDur,",",round(cDur_se),")") ),size=8, hjust=0.5, vjust=-2, color = 'black')+
  labs(x = " ", y = " ") +
  #coord_cartesian(ylim = c(0,1600))+
  scale_color_manual(values = c('gray','black')) +
  scale_fill_manual(values = c('gray','black')) +
  theme(legend.position = "none", legend.title = element_blank())+
  theme(panel.grid.major=element_line(colour=NA))+
  theme(axis.text.y = element_text(size=26,colour = "black"),
        axis.text.x   = element_text(size=26, colour = "black"),
        axis.title.y  = element_text(size=26, colour = "black"),
        axis.title.x  = element_text(size=26, colour = "black"),
        panel.background = element_blank(),
        panel.grid.major = element_blank(),
        panel.grid.minor = element_blank(),
        axis.line = element_line(colour = "black")
  )
if (saveFigure == TRUE){
  ggsave("figures/plot_mDist_exp2.png", plot_mDist_exp2, width = 5, height = 5.5)
}
plot_mDist_exp2

Fit psychometric functions

fits_exp2 = quickpsy(dat_exp2, x = curDur, k =RP, prob = .5, grouping = .(cond, NSub))

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fits_exp2_all = quickpsy(dat_exp2, x = curDur, k =RP, 
                         grouping = .(cond))
fits_exp2_all

NULL

# plot fitted function
plot_fit_exp2 <- plot(fits_exp2_all) + 
  labs(x = "Durations (ms)", y = "Proportion of 'Long' responses") +
  scale_color_manual(values = c('gray','black')) +
  scale_fill_manual(values = c('gray','black')) +
  theme(legend.position = c(0.7, 0.2), legend.title = element_blank())

Ignoring unknown aesthetics: x

plot_fit_exp2

Average fitted paramters and plot

par_exp2 = fits_exp2$par %>% 
  dplyr::select(-parinf,-parsup) %>%
  spread(parn, par) %>%   
  rename(pse =p1, jnd = p2)  # rename columns

par_exp2$slope = 3/exp(par_exp2$pse/1000) #add slope

par_exp2

mpse_exp2 = par_exp2%>% 
  group_by(cond) %>%
  summarise(m_pse = mean(pse), m_jnd = mean(jnd), m_slope = mean(slope), n = n(),
            pse_se = sd(pse)/sqrt(n-1), 
            jnd_se = sd(jnd)/sqrt(n-1),
            slope_se = sd(slope)/sqrt(n-1)) 
mpse_exp2

Export for JASP

List all of the parameters for Exp2 and export data for JASP

exp2_jasp <- par_exp2%>% 
  unite(pse.jnd.slope, pse, jnd, slope)%>%
  spread(cond, pse.jnd.slope)%>%
  separate(DF, c("DF_pse", "DF_jnd","DF_slope"), sep = "_")%>%
  separate(AF, c("AF_pse", "AF_jnd", "AF_slope"), sep = "_")

exp2_jasp

plot PSE

plot_pse_exp2 <- ggplot(mpse_exp2,aes(cond, m_pse, color = cond, fill = cond))+
  geom_bar(stat='identity') + 
  geom_errorbar(aes(ymin = m_pse - pse_se, ymax = m_pse + pse_se), width =0.5) +
  geom_signif(comparisons=list(c("DF", "AF")), annotations="***", y_position = 1250, tip_length = 0, vjust=0.4, color = 'black') +
  labs(x = " ", y = "Mean PSE (ms)") +
  coord_cartesian(ylim = c(0,1300))+
  scale_color_manual(values = c('gray','black')) +
  scale_fill_manual(values = c('gray','black')) +
  theme(legend.position = "none")

plot_pse_exp2

plot JND

plot_jnd_exp2 <- ggplot(mpse_exp2,aes(cond, m_jnd, color = cond, fill = cond))+
  geom_bar(stat='identity') + 
  geom_errorbar(aes(ymin = m_jnd - jnd_se, ymax = m_jnd + jnd_se), width =0.5) +
  geom_signif(comparisons=list(c("DF", "AF")), annotations="***", y_position = 330, tip_length = 0, vjust=0.4, color = 'black') +
  labs(x = " ", y = "Mean JND (ms)") +
  coord_cartesian(ylim = c(0,350))+
  scale_color_manual(values = c('gray','black')) +
  scale_fill_manual(values = c('gray','black')) +
  theme(legend.position = "none")

plot_jnd_exp2

ANOVA

Anova_exp2_pse <- ezANOVA(data = par_exp2, dv= pse, wid=NSub, within=.(cond))

Converting "NSub" to factor for ANOVA.

Anova_exp2_pse

$ANOVA

NA

Anova_exp2_jnd <- ezANOVA(data = par_exp2, dv= jnd, wid=NSub, within=.(cond))

Converting "NSub" to factor for ANOVA.

Anova_exp2_jnd

$ANOVA

NA

Anova_exp2_slope <- ezANOVA(data = par_exp2, dv= slope, wid=NSub, within=.(cond))

Converting "NSub" to factor for ANOVA.

Anova_exp2_slope

$ANOVA

NA

Range Frequency Theory

To understand the pattern of results concerning schifts in the temporal bisection point, We have to check the distribution of stimuli within the sets firstly.

sumfreq_exp3_sub1 <-  dat_exp3 %>% filter(NSub ==1) %>% group_by(cond, curDur) %>% summarise(count = n()) 
# rename columns
sumfreq_exp3_sub1$exp <- 'Exp3'
count_exp3 <- sum(sumfreq_exp3_sub1$count)/2
sumfreq_exp3_sub1$freq <- sumfreq_exp3_sub1$count/count_exp3*100

fig_exp3_sub1_dist <- ggplot(data=sumfreq_exp3_sub1, aes(x=curDur, y=freq, fill=cond)) +
  geom_bar(stat="identity", position=position_dodge()) + 
  xlab('Durations (ms)') + ylab('Counts of trials for each participant') +
  scale_x_continuous(breaks=seq(0, 1600, 200)) +
  scale_color_manual(values = c('gray','black')) +
  scale_fill_manual(values = c('gray','black')) +mytheme

fig_exp3_sub1_dist

mDist_exp3 <-  dat_exp3 %>% filter(NSub == 1) %>% dplyr::group_by(cond) %>%
  summarise(m_cDur = mean(curDur), n = dplyr::n(),
            cDur_se = sd(curDur)/sqrt(n-1))
mDist_exp3

plot_mDist_exp3 <- ggplot(mDist_exp3,aes(cond, m_cDur, color = cond, fill = cond))+
  geom_bar(stat='identity') +
  geom_errorbar(aes(ymin = m_cDur - cDur_se, ymax = m_cDur + cDur_se), width =0.5) +
   labs(x = " ", y = " ") +
  scale_color_manual(values = c('gray','black')) +
  scale_fill_manual(values = c('gray','black')) +
  theme(legend.position = "none", legend.title = element_blank())+
  theme(panel.grid.major=element_line(colour=NA))+
  theme(axis.text.y = element_text(size=26,colour = "black"),
        axis.text.x   = element_text(size=26, colour = "black"),
        axis.title.y  = element_text(size=26, colour = "black"),
        axis.title.x  = element_text(size=26, colour = "black"),
        panel.background = element_blank(),
        panel.grid.major = element_blank(),
        panel.grid.minor = element_blank(),
        axis.line = element_line(colour = "black"))
plot_mDist_exp3

Fit psychometric functions

fits_exp3 = quickpsy(dat_exp3, x = curDur, k =RP, prob = .5,
                     grouping = .(cond, NSub), thresholds = FALSE)

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fits_exp3_all = quickpsy(dat_exp3, x = curDur, k =RP, 
                         grouping = .(cond), thresholds = FALSE)
fits_exp3_all

NULL

# plot fitted function
plot_fit_exp3 <- plot(fits_exp3_all) +  
  labs(x = "Durations (ms)", y = "Proportion of 'Long' responses") +
  scale_color_manual(values = c('gray','black')) +
  scale_fill_manual(values = c('gray','black')) +
  theme(legend.position = c(0.7, 0.2), legend.title = element_blank())

plot_fit_exp3

List all of the parameter for each subjects

par_exp3 = fits_exp3$par %>% 
  dplyr::select(-parinf,-parsup) %>%
  spread(parn, par) %>%   
  rename(pse =p1, jnd = p2)  # rename columns

par_exp3$slope = 3/exp(par_exp3$pse/1000) #add slope

par_exp3

mpars_exp3 = par_exp3%>% 
  group_by(cond) %>%
  summarise(m_pse = mean(pse), m_jnd = mean(jnd), m_slope = mean(slope), n = n(),pse_se = sd(pse)/sqrt(n-1), jnd_se = sd(jnd)/sqrt(n-1),slope_se = sd(slope)/sqrt(n-1))

mpars_exp3

##Export for JASP

List all of the parameters for Exp3 and export data for JASP

exp3_jasp <- par_exp3%>% 
  unite(pse.jnd.slope, pse, jnd, slope)%>%
  spread(cond, pse.jnd.slope)%>%
  separate(`U-shaped`, c("U_pse", "U_jnd", "U_slope"), sep = "_")%>%
  separate(`I T-shaped`, c("B_pse", "B_jnd", "B_slope"), sep = "_")

exp3_jasp

plot PSE

plot_pse_exp3 <- ggplot(mpars_exp3,aes(cond, m_pse, color = cond, fill = cond))+
  geom_bar(stat='identity') + 
  geom_errorbar(aes(ymin = m_pse - pse_se, ymax = m_pse + pse_se), width =0.5) +
  coord_cartesian(ylim = c(0,1300)) +
  labs(x = " ", y = "Mean PSE (ms)") +
  scale_color_manual(values = c('gray','black')) +
  scale_fill_manual(values = c('gray','black')) +
  theme(legend.position = "none", legend.title = element_blank())
plot_pse_exp3

plot JND

plot_jnd_exp3 <- ggplot(mpars_exp3,aes(cond, m_jnd, color = cond, fill = cond))+
  geom_bar(stat='identity') + 
  geom_errorbar(aes(ymin = m_jnd - jnd_se, ymax = m_jnd + jnd_se), width =0.5) +
  coord_cartesian(ylim = c(0,300))+
  geom_signif(comparisons=list(c("U-shaped", "I T-shaped")), annotations="***", y_position = 250, tip_length = 0, vjust=0.4, color = 'black') +
  labs(x = " ", y = "Mean JND (ms)") +
  scale_color_manual(values = c('gray','black')) +
  scale_fill_manual(values = c('gray','black')) +
  theme(legend.position = "none")
plot_jnd_exp3

ANOVA

Anova_exp3_pse<- ezANOVA(data = par_exp3, dv= pse, wid=NSub, within=.(cond))

Converting "NSub" to factor for ANOVA.

Anova_exp3_pse

$ANOVA

NA

Anova_exp3_jnd<- ezANOVA(data = par_exp3, dv= jnd, wid=NSub, within=.(cond))

Converting "NSub" to factor for ANOVA.

Anova_exp3_jnd

$ANOVA

NA

Anova_exp3_slope<- ezANOVA(data = par_exp3, dv= slope, wid=NSub, within=.(cond))

Converting "NSub" to factor for ANOVA.

Anova_exp3_slope

$ANOVA

NA

plot figure 1 in manuscript

fig_exp1_sub1_dist2 <- ggplot(data=sumfreq_exp1_sub1, aes(x=curDur, y=freq, fill=cond, color = cond)) +
  geom_bar(stat="identity", position=position_dodge(),width = 3) + 
  geom_point()+
  xlab('') + ylab('Prob. (%)') +
  scale_x_continuous(breaks=seq(0, 1600, 200)) +
  scale_y_continuous(breaks=seq(0, 50, 5)) +
  scale_color_manual(values = c('gray','black')) +
  scale_fill_manual(values = c('gray','black')) +
  theme(legend.position = "none", legend.title = element_blank()) + facet_wrap(~cond)

fig_exp2_sub1_dist_2 <- ggplot(data=sumfreq_exp2_sub1, aes(x=curDur, y=freq, fill=cond, color = cond)) +
  geom_bar(stat="identity", position=position_dodge(), width = 3) + 
  geom_point()+
  scale_x_continuous(breaks=seq(0, 1600, 200)) +
  scale_y_continuous(breaks=seq(0, 50, 10)) +
  xlab('') + ylab('Prob. (%)') +
  scale_color_manual(values = c('gray','black')) +
  scale_fill_manual(values = c('gray','black')) +
  theme(legend.position = 'none', legend.title = element_blank()) + facet_wrap(~cond)

fig_exp3_sub1_dist2 <- ggplot(data=sumfreq_exp3_sub1, aes(x=curDur, y=freq, fill=cond, color = cond)) +
  geom_bar(stat="identity", position=position_dodge(), width = 3) + 
  geom_point()+
  xlab('Durations (ms)') + ylab('Prob. (%)') +
  scale_x_continuous(breaks=seq(0, 1600, 200)) +
  scale_y_continuous(breaks=seq(0, 50, 10)) +
  scale_color_manual(values = c('gray','black')) +
  scale_fill_manual(values = c('gray','black')) +
  theme(legend.position = "none", legend.title = element_blank())+ facet_wrap(~cond)

plot_grid(fig_exp1_sub1_dist2, fig_exp2_sub1_dist_2, fig_exp3_sub1_dist2,  ncol = 1, labels = c("A", "B", "C"), rel_heights = c(3,3,3))

plot Figure 2 in manuscript

plot_grid(plot_fit_exp1, plot_pse_exp1, plot_jnd_exp1,  nrow = 1, labels = c("A", "B", "C"), rel_widths = c(4,3,3))

plot Figure 3 in manuscript

plot_grid(plot_fit_exp2, plot_pse_exp2, plot_jnd_exp2,  nrow = 1, labels = c("A", "B", "C"), rel_widths = c(4,3,3))

plot Figure 4 in manuscript

plot_grid(plot_fit_exp3, plot_pse_exp3, plot_jnd_exp3,  nrow = 1, labels = c("A", "B", "C"), rel_widths = c(4,3,3))

load the Model result

#customize theme
theme_new <- theme_bw() + 
  theme(panel.border = element_blank(), 
        panel.grid.major = element_blank(),
        panel.grid.minor = element_blank(), 
        axis.line=element_line(colour="black"),
        strip.background = element_rect(color = "white", fill = "white"),
        panel.grid = element_blank())

models <- c('model1', 'model2','model3', 'model4','model5')
expDat <- list(dat_exp1, dat_exp2, dat_exp3)
#load the data and remove the outliers
par_GLM_observed <-read.csv('../data/par_observed.csv') %>% filter(!((NSub == 10|NSub == 6 ) & (cond == 'AF'| cond =='DF')))%>% filter(!((NSub == 1) & (cond == 'PS'| cond =='NS')))
modelresults<- read.csv("../data/modelresults.csv")  %>% filter(!((NSub == 10|NSub == 6) & (cond == 'AF'| cond =='DF')))%>% filter(!((NSub == 1) & (cond == 'PS'| cond =='NS')))

displayModellist <- c("Bisection Model",  "Spacing Model", "Ensemble Mean",  "Two-stage Ensemble Mean", "EDA")
#combine oberserved and predicated PSEs and JNDs
par_comb = left_join(modelresults, par_GLM_observed, by = c('NSub', 'cond')) 
par_comb$errpse <- par_comb$PSEmap-par_comb$pse
par_comb$errjnd <- par_comb$JNDmap-par_comb$jnd
par_comb$model = factor(par_comb$model, labels = displayModellist)
head(par_comb)

NA

#calculate AIC and BIC
numParam <- 3
mpar_comb <- par_comb %>% dplyr::group_by(model, cond) %>%
  dplyr::summarise(sumerrpse=sum((errpse)^2), n=n(), 
                   sumerrjnd=sum((errjnd)^2)) %>% 
  dplyr::group_by(model, cond) %>%
  summarise(aicPse= 2 * numParam +  n*log(sumerrpse/n),
            bicPse = n*log(sumerrpse/n) + numParam*log(n),
            aicJnd= 2 * numParam +  n*log(sumerrjnd/n),
            bicJnd = n*log(sumerrjnd/n) + numParam*log(n), ) 

### show the mean in each model 
m_par <- modelresults %>% group_by(model, cond, NSub) %>%
  summarise(xmean= mean(xmean), xmeanhat= mean(xmeanhat))  %>%
  group_by(model, cond) %>%
  summarise(xmean= mean(xmean), xmeanhat= mean(xmeanhat)) 

plot figure 7 in manuscript

par_comb <- arrange(transform(par_comb,
                              cond=factor(cond,levels=c("PS","DF","U-shaped","NS","AF","I T-shaped"))),cond)

cbp1 <- c( "#CC79A7", "#F0E442", "#0072B2", "#E69F00", "#D55E00")
plt_ErrorScatter = ggplot(par_comb, aes(errpse, errjnd, color = model, shape = model)) + 
  geom_hline(yintercept = 0, linetype='dashed')+ geom_vline(xintercept = 0, linetype='dashed')+ 
  geom_point() +
  xlab('Prediction error in the PSEs (ms)')+ ylab('Prediction error in the JNDs (ms)')+
  scale_color_manual(values = cbp1) +
  scale_shape_manual(values=c(0, 1, 2, 8, 16))+
  facet_wrap(~cond)+
  theme_new+ theme(legend.position = 'top')

plt_ErrorScatter

plot figure 6 in manuscript

m_parcomb <- par_comb %>% dplyr::group_by(model, cond) %>%
  dplyr::summarise(mPSEmap=mean(PSEmap), pse = mean(pse), mJNDmap=mean(JNDmap),jnd = mean(jnd),
                   merrpse =mean(errpse), merrjnd = mean(errjnd),n=n(), 
                   PSEmap_se = sd(PSEmap)/sqrt(n-1), JNDmap_se = sd(JNDmap)/sqrt(n-1),
                   errpse_se =sd(errpse)/sqrt(n-1), errjnd_se =sd(errjnd)/sqrt(n-1)) 

m_par_observed <- par_GLM_observed %>% dplyr::group_by(cond) %>%
  dplyr::summarise(mpse=mean(pse), mjnd= mean(jnd), n=n(), 
                   pse_se =sd(pse)/sqrt(n-1), jnd_se =sd(jnd)/sqrt(n-1)) 
m_par_observed$mPSEmap<-m_par_observed$mpse 
m_par_observed$mJNDmap<-m_par_observed$mjnd 

m_parcomb2 <- arrange(transform(m_parcomb,
                                cond=factor(cond,levels=c("PS","DF","U-shaped","NS","AF","I T-shaped"))),cond)


fig_estimation = ggplot(m_parcomb2, aes(x=mPSEmap, y=mJNDmap, color = model)) + 
  geom_point(data =m_par_observed, aes(x = mpse, y =mjnd, size=2), width =2, shape =16, alpha = 0.5,  color = 'black') +
  geom_point(data = par_comb, aes(x = pse, y =jnd), alpha = 0.25, color = 'lightgray') +
  geom_point() +
  geom_errorbar(aes(ymax=mJNDmap+JNDmap_se, ymin=mJNDmap-JNDmap_se), size=0.6)+
  geom_errorbarh(aes(xmax=mPSEmap+PSEmap_se, xmin=mPSEmap-PSEmap_se),size=0.6)+
  ylab('Observed JNDs (ms)')+xlab('Observed PSEs (ms)') +
  scale_color_manual(values = cbp1) +
  theme_new+ theme(legend.position = 'top') + 
  facet_wrap(.~cond,  ncol=3)+
  scale_size(guide = 'none')

Ignoring unknown parameters: width

#+xlim(600,1200)+ylim(45,200)
fig_estimation